Some convergence results for inexact Radau IIA methods applied to evolutionary PDEs.

The convergence of a family of AMF-Radau methods for the time integration of evolutionary semilinear Partial Dierential Equations (PDEs) of Advection Diusion Reaction type semi-discretized in space is considered. The methods are based on very few inexact Newton Iterations of Aproximate Matrix Factorization type (AMF) applied to the two-stage Radau IIA method. Uniform bounds for the global timespace errors on semi-linear PDEs when simultaneously the time stepsize and the spatial grid resolution tend to zero are derived. Numerical illustrations supporting the theory are presented.